The single‐component adaptive Metropolis (SCAM) algorithm, as one of the Markov chain Monte Carlo (MCMC) sampling methods, is very effective at solving high‐dimensional posterior joint probability distributions. However, studies show that the SCAM algorithm is prone to generating duplicate samples, thus lowering the sampling efficiency and causing large calculation errors. To solve this problem, a modified SCAM algorithm is proposed in the present study. In the modified algorithm, the expression of the variance of the proposal distribution is redefined so that the Markov chain formed by the sample sequence is relatively stable. With the obtained structural response, the posterior joint probability distribution of the physical parameters of the structure is achieved using Bayesian theory, which is then combined with the modified SCAM algorithm to solve the posterior marginal probability distribution and the optimal estimates. Hence, the structural damage is identified. The validity, reliability, and practicability of the modified SCAM algorithm are verified through theoretical analysis, a numerical simulation of the structural example, and a shaking table test. The results show that the modified SCAM algorithm not only enhances the accuracy of the calculation results but also increases the sampling efficiency. This method can be used as a reference for physical parameter identification and damage assessment of the engineering structures.

中文翻译：

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基于改进SCAM算法的贝叶斯估计方法及其在结构损伤识别中的应用

作为马尔可夫链蒙特卡洛（MCMC）采样方法之一的单分量自适应都会（SCAM）算法在求解高维后验联合概率分布方面非常有效。然而，研究表明，SCAM算法易于生成重复样本，从而降低了采样效率并导致较大的计算误差。为了解决这个问题，本文提出了一种改进的SCAM算法。在改进的算法中，重新定义提议分布的方差表达式，以使样本序列形成的马尔可夫链相对稳定。利用获得的结构响应，使用贝叶斯理论获得结构物理参数的后关节概率分布，然后将其与改进的SCAM算法结合，以解决后验边际概率分布和最优估计。因此，确定了结构损坏。通过理论分析，结构实例的数值模拟和振动台试验，验证了改进后的SCAM算法的有效性，可靠性和实用性。结果表明，改进的SCAM算法不仅提高了计算结果的准确性，而且提高了采样效率。该方法可以作为物理参数识别和工程结构损伤评估的参考。通过理论分析，结构实例的数值模拟和振动台试验，验证了改进后的SCAM算法的可行性和实用性。结果表明，改进的SCAM算法不仅提高了计算结果的准确性，而且提高了采样效率。该方法可以作为物理参数识别和工程结构损伤评估的参考。通过理论分析，结构实例的数值模拟和振动台试验，验证了改进后的SCAM算法的可行性和实用性。结果表明，改进的SCAM算法不仅提高了计算结果的准确性，而且提高了采样效率。该方法可以作为物理参数识别和工程结构损伤评估的参考。